Optical communication system having enhanced spectral efficiency using electronic signal processing

ABSTRACT

An optical communication system combines strong electrical pre-filtering of data at the transmitter and digital feedback equalization (DFE) at the receiver to enhance spectral efficiency. The system can be applied to optical networking and digital communication systems, including binary modulated systems optical network systems.

RELATED APPLICATIONS

This application claims priority to U.S. Patent Application No.60/799,244, filed May 10, 2006, the disclosure of which is herebyincorporated by reference.

TECHNICAL FIELD

The invention relates to fiber optic communications and opticalcommunication systems, such as metropolitan optical networks or thelike.

BACKGROUND

Fiber optic communication generally involves modulating optical signalsat high bit rates and transmitting the modulated optical signals overoptical fibers. For example, in a wavelength division multiplexed (WDM)fiber optic communications system, optical carrier signals at a sequenceof distinct wavelengths are separately modulated by information channelsand then multiplexed onto a single optical fiber. Efforts continuetoward increasing the data capacity of fiber optic communicationssystems.

One of the key features of a wavelength division multiplexed (WDM)system is spectral efficiency, which determines how many bits/sec ofdata can be transmitted per unit of available bandwidth. The availablebandwidth in practical WDM systems is limited by optical amplifierswhich are used to periodically boost the optical power for a giventransmission length. However, upgrading the capacity of existing opticalnetworks by replacing in-ground fiber and amplifiers is extremelycostly. Various techniques have been proposed to enhance the spectralefficiency of WDM systems to improve spectral efficiency (i.e., bits persecond transmitted per unit of available bandwidth) of the existingoptical infrastructure. That is, because of the cost associated withupgrading or replacing the available WDM bandwidth, various techniqueshave been proposed to enhance the spectral efficiency of WDM systems toapproach or exceed 1 bit/sec/Hz, which is the theoretical limit for asimple binary modulation format.

However, most of these techniques involve either complex binarymodulation formats to limit the channel bandwidth for a given data rate,or an attempt to take advantage of multi-level modulation formats andpolarization division multiplexing to increase the spectral efficiency.However, many of these complex techniques require costly transmittersand receivers with specialized, expensive electronics.

SUMMARY

In general, techniques are described herein for combining strongelectrical pre-filtering of data at a transmitter with digital feedbackequalization (DFE) at a receiver to enhance the spectral efficiency offiber optic communication. The techniques can be applied to opticalnetworking and digital communication systems, including binary NRZintensity modulated systems optical network systems.

In certain embodiments, pre-filtering of each data channel at thetransmitter is accomplished using an electrical low pass filter (LPF)before optical intensity modulation in order to limit the channelbandwidth. That is, in order to limit the frequency spreading of thedata channels, each data channel is pre-filtered prior to any modulationand multiplexing of the data channels into the fiber link. Thispre-filtering effectively “clips” the frequency spreading of each of thedata channels in the frequency domain, and allows for reduced channelspacing at the transmitter. As a result, the data channels can be“packed” closer within the frequency spectrum, thereby enhancingspectral efficiency of the optical transmission.

However, the incorporation of the pre-filtering at the transmitterinduces severe inter-symbol interference (ISI) in each WDM channel.Therefore, DFE is employed at the receiver to electronically compensatefor the ISI that was induced by strong pre-filtering of individualchannels at the transmitter. In other words, DFE within the receiver isused to compensate for signal distortion that was intentionallyintroduced at the transmitter prior to optical transmission in order toreduce channel spacing, as opposed to compensation for ISI or othereffects introduced by transmission through the optical channel. In thismanner, pre-filtering at the transmitter and equalization at thereceiver may be utilized in combination so as to enhance the spectralefficiency of a WDM system.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features,objects, and advantages of the invention will be apparent from thedescription and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of the WDM system employing pre-filter attransmitter and decision feedback equalizer at receiver. LD is a laserdiode, PD is a photo-detector, DC is a decision circuit and T is a bittime delay. Please note that λ₁ to λ_(n) are at orthogonalpolarizations.

FIG. 2 is a graph showing the eye opening vs. number of feed forward tapfilters for different numbers of feedback tap filters. Spectralefficiency is 1 bit/sec/Hz.

FIG. 3 is a graph showing eye opening vs. spectral efficiency with andwithout proposed scheme for a back to back 10.7 Gb/s WDM system. Theeyes in the right hand side are (i) with pre-filtering+DFE, (ii) withpre-filtering but no DFE, and (iii) without pre-filtering and no DFE.

FIG. 4 is a block diagram showing a simulated fiber link employing atypical terrestrial dispersion map using standard single mode fiber andErbium doped fiber amplifiers.

FIG. 5 is a graph showing eye opening vs. average channel power forspectral efficiencies of 1.6 bit/sec/Hz (circles) and 1.0 bit/sec/Hz(squares). Solid circles and squares represent the proposed scheme andhollow circles and squares represent the ordinary WDM system.

FIG. 6 is a graph showing Q Factor vs. average channel power forspectral efficiencies of 1.6 bit/sec/Hz with 400 km transmissiondistance and 1.0 bit/sec/Hz with 800 km transmission distance.

FIG. 7 is a graph showing a comparison of system Q for bit synchronousand fractionally spaced (FF tapped delay=T/3) DFE for 400 km system withspectral efficiency of 1.6 bit/sec/Hz and 800 km system with spectralefficiency of 1.0 bit/sec/Hz.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of an example communication system 2 employingthe electronic signal processing techniques to enhance spectralefficiency. At the transmitter 4, a filter 3, e.g., an electrical lowpass filter (LPF), is used to pre-filter each data channel (data) bylimiting the bandwidth of each data channel prior to modulation. In oneembodiment, a Bessel shaped LPF of order 10 is used for pre-filtering.The 3-dB bandwidth of the pre-filter may be selected to reduce orminimize the crosstalk for a given channel spacing. The desired 3-dBbandwidth of the pre-filter may be 3.5 GHz for a spectral efficiency of1 bit/sec/Hz (channel spacing=10 GHz). After pre-filtering, each datachannel is optically modulated by a modulator (Mod), such as aMach-Zehnder Interferometer (MZI) based modulator or other form ofmodulator suitable for optical communication. All the modulated channelsare then multiplexed (MUX) together for transmission into the fiber link5.

As one example, in one embodiment, 11 channels may be multiplexed withorthogonal polarizations of alternate wavelengths at the data rate of10.7 Gb/s each to have an effective spectral efficiency of 1 bit/sec/Hz.A 10.7 Gb/s data rate can be used to include 7% forward error correction(FEC) overhead. To evaluate the effectiveness of the technique inback-to-back configuration, receiver 6 includes a bandpass filter (BPF)to demultiplex the middle of 11 simulated channels (FIG. 1). As oneexample, a 2^(nd) order Gaussian shaped bandpass filter (BPF) may beused with 3-dB bandwidth of 11 GHz, which can be tuned to limit thecrosstalk for 10 GHz channel spacing with orthogonally launched adjacentchannels.

After BPF, the optical signal is photo-detected (PD) and passed throughan electrical LPF, e.g., an LPF with 3-dB bandwidth of 7.5 GHz. FIG. 1shows one example in which, after LPF, an eye diagram 7 of the middlechannel, where the eye diagram is a graph that superimposes data bitsreceived versus time. Severe ISI induced by pre-filtering can be seen ineye diagram 7, which is due to distortion (i.e., ISI) introduced by theintentional pre-filtering of each data channel by filter 3. In theexample of FIG. 1, Receiver 6 includes a decision feedback equalizer(DFE) 10 comprising n feed forward (FF) and m feedback (FB) tapped delayfilters 12 to compensate for the ISI introduced by filter 3. Bitsynchronous tapped delay filters i.e., the delay is one bit time (T),may be used. Other equalizers could be used, e.g., Maximum SequenceLikelihood Estimation (MSLE) or Viterbi Decoding, to compensate for theISI resulting from the intentional pre-filtering at the transmitter 4.

In one embodiment, the coefficients (d₁ . . . d_(m), c₀ . . . c_(n)) maybe adaptive. For example, the coefficients (d₁ . . . d_(m), c₀ . . .c_(n)) of FF and FB tapped delay filters may be adapted by sending along sequence of randomly generated bits and using the least mean square(LMS) algorithm until the coefficients become stationary. The weights ofthe coefficients can be represented by a vector {right arrow over(C)}=[c₀, c₁, . . . , c_(n), d₁, d₂, . . . d_(m)]. The LMS algorithmupdates {right arrow over (C)} with each incoming bit:{right arrow over (C)} ^((k+1)) ={right arrow over (C)} ^((k+1))+Δ_(k){right arrow over (V)} ^((k))  (1),where {right arrow over (C)}^((k)) represents the tap vector weights attime kT, Δ is the scale factor that controls the rate of adaptation andε_(k) is the error signal between the decision sample and the decisionoutput. The vector {right arrow over (V)}=[v_(k), v_(k−1), . . . ,c_(k−(n−n)), I_(k−1)), d_(k−2), . . . , d_(k−m)], where v_(k−i) is theinput signal at time (k−i)T and I_(k−i) is the decision made at time(k−i)T.

Alternatively, since DFE 10 is being used to compensate for a known,intentional level of signal distortion resulting from filter 3 oftransmitter 4, the coefficients (d₁ . . . d_(m), c₀ . . . c_(n)) may bepre-computed, thereby conversing computation resources and reducingcomplexity of receiver 6. That is, coefficients (d₁ . . . d_(m), c₀ . .. c_(n)) need not be adaptive based on an error signal, but rather setas a function of the amount of distortion that was intentionallyintroduced at the transmitter in order to tightly pack the data channelswithin the optical transmission. These stationary coefficients in DFE 10of receiver 6 (as shown in FIG. 1) can be used to equalize the ISIinduced by the pre-filtering of the channels at transmitter 4.

In the example of FIG. 1, a different sequence of 2¹³ pseudorandom bitscan be used to obtain an eye diagram 9 just before the sampler for thedecision circuit (part of the DFE). Eye diagram 9 of the middle channelis also shown in FIG. 1 (left of the two) using 8 FF and 2 FB tappeddelay filters. More than 90% eye opening, as shown in eye diagram 9,shows that ISI induced by pre-filtering can be very efficientlycompensated, proving the effectiveness of the technique of combiningpre-filtering at transmitter and DFE at the receiver to enhance thespectral efficiency binary intensity modulated systems.

In the example of FIG. 1, the eye diagram 9 of FIG. 1 can be producedusing 8 FF and 2 FB tapped delay filters. FIG. 2 illustrates examplecriteria for choosing a desirable number of FF and FB tapped delayfilters for DFE 10 in which eye opening of 10 GHz spaced system is shownversus number of FF tapped delay filters for 0, 2 and 4 FB tapped delayfilters. One can see from FIG. 2 that effectiveness of DFE improves withincreasing the number of FF tapped delay filters up to 8 beyond whichthe improvement in performance saturates.

Similarly, FIG. 2 also shows that increasing the FB tapped delay filtersbeyond 2 does not bring any further improvement for a 10 GHz spacedsystem. The optimum number of tapped delay filters may depend upon theamount of ISI to be compensated, and therefore may depend upon thechannel spacing (spectral efficiency) for which pre-filtering bandwidthis optimized. That is, the number of n feed forward (FF) and m feedback(FB) tapped delay filters 12 can be selected as a function of an amountof filtering applied by the filter 3 of the transmitter 4, whichdirectly relates to the channel spacing that may be used by transmitter4. Similarly, one can perform the same analysis with a 6.25 GHz spacedsystem and determine that acceptable performance can be achieved byusing 8 FF and 4 FB tapped delay filters. For the 6.25 GHz spacedfilter, for example, an optimized pre-filter bandwidth may beapproximately 2.5 GHz.

The back-to-back system performance can be analyzed by varying thespectral efficiency both with and without pre-filtering and DFE.Exemplary results of such an analysis are shown in FIG. 3 in which eyeopening is plotted vs. spectral efficiency with and withoutpre-filtering and DFE. At lower spectral efficiency of 0.4 bit/sec/Hz(channel spacing=25 GHz), performance with the use of pre-filtering andDFE is only slightly better than a regular NRZ WDM system because thecrosstalk is small at such a large channel spacing. However when thespectral efficiency is increased, the crosstalk increases due to reducedchannel spacing and hence severely degrades the performance of regularNRZ WDM system. At high spectral efficiency the technique usingpre-filtering and DFE improves the system performance significantly byalmost completely eliminating the crosstalk using pre-filtering andefficiently compensating the resulting ISI using DFE. At the spectralefficiency of 1.6 bit/sec/Hz, the eye may be completely closed withoutusing pre-filtering and DFE showing the system may not work with regularNRZ WDM scheme, whereas the pre-filtering and DFE may open thecompletely closed eye by more than 50%. Notably, a pre-filtered eyediagram without DFE at the spectral efficiency of 1.6 bit/sec/Hz is alsoshown in FIG. 3. The pre-filtered eye is also fully closed but not dueto crosstalk but rather due to severe ISI induced by a narrowpre-filtering with the bandwidth of 2.5 GHz which is optimized for 6.25GHz channel spacing. This ISI can be partially compensated using DFE andthereby opening the eye by more than 50%.

After back-to-back analysis, we analyzed the performance of thepre-filtering and DFE scheme by transmitting through a typicalterrestrial dispersion map based upon SSMF shown in FIG. 4. Thedispersion map consisted of 100 km spans of SSMF followed by a two stageEDFA having 20 km of dispersion compensating fiber (DCF) in between thetwo stages to compensate the dispersion of each span. The path averagedispersion was assumed to be non-zero (−0.5 ps/nm-km per span) and wascompensated using a fixed post-dispersion compensation at the receiver.The total span loss including the DCF is 35 dB and the noise figure ofeach EDFA was 6 dB. The dispersion values of SMF and DCF were 17 and −85ps/nm-km, respectively. The effective areas of SMF and DCF were assumedto be 75 and 20 μm².

An independent pseudorandom bit stream of 2¹³ bits was transmitted oneach of 11 channels through this dispersion map using pre-filtering atthe transmitter and DFE at the receiver. Propagation of a wavelengthmultiplexed signal was simulated by solving nonlinear Schrodingerequation using split step Fourier scheme. The simulated nonlineareffects are self-phase modulation (SPM), cross-phase modulation (XPM)and four-wave mixing (FWM). In the first step we ignored the amplifiedstimulated emission (ASE) noise and carried out noiseless simulation toestimate the performance of pre-filtering and DFE in presence of fibernonlinearity.

The resulting eye opening of the middle channel vs. averagepower/channel is shown in FIG. 5 for the transmission distance of 400 kmwith spectral efficiency of 1.6 bit/sec/Hz and for the transmissiondistance of 800 km with the spectral efficiency of 1 bit/sec/Hz. A totalof 11 channels were simulated to ensure that XPM due to neighboringchannels was properly included (5 significant neighboring channels oneach side). We varied the number of simulated channels from 3 to 19 andfound that the WDM nonlinear penalty due to XPM and FWM did notsignificantly increase when WDM channels are increased beyond 11. Forcomparison purpose, the eye opening as a result of no pre-filtering andno DFE is also shown in FIG. 5 for the corresponding distances andspectral efficiencies. We can see that the eye opening decreases withincreasing channel power due to fiber nonlinearities but still performssignificantly better than the case without pre-filtering and DFE. Thespectral efficiency of 1.6 bit/sec/Hz, the eye was totally closedwithout using pre-filtering and DFE due to severe inter-channelcrosstalk. Similarly, at the spectral efficiency of 1 bit/sec/Hz, theeye was less than 30% open without using the pre-filtering and DFE andwas mainly degraded by crosstalk rather than nonlinearity. Therefore,eye opening decreases slowly with increasing channel power.

To estimate the bit error rate (BER) performance, we analyzed the abovesystem by adding the accumulated noise at the receiver just before thephoto-detection. We repeated the full receiver processing including DFEone hundred times by adding different optical noise each time. We thenobtained the average and standard deviation of each bit just before thedecision circuit in DFE. By assuming the Gaussian noise distribution, aBER was then calculated for each bit and then an average BER wasobtained. The average BER was then converted to a Q factor. Theresulting Q factors for the WDM systems with spectral efficiencies of1.6 bit/sec/Hz (400 km system) and 1.0 bit/sec/Hz (800 km system) areshown in FIG. 6 vs. average channel power. The Q factor increases withincreasing channel power due to better signal-to-noise ratio (SNR) andbeyond a certain channel power, fiber nonlinearity increases too muchand degrades the system performance. The optimal Q's of 14.1 and 16 dBare obtained respectively for the transmission distance of 400 km with1.6 bit/sec/Hz spectral efficiency and 800 km with 1.0 bit/sec/Hz ofspectral efficiency. We used an FEC overhead of 7% which will give anadditional gain in Q of at least 5 dB. This suggests the feasibility ofa 1.6 bit/sec/Hz of spectral efficiency for metropolitan distances usingthe pre-filtering and DFE technique.

Next, the performance of fractionally spaced DFE in improving spectralefficiency was compared to bit synchronous DFE. In bit synchronous DFE,both FF and FB tapped delay filters use a delay of one bit time (T). Onthe contrary, fractionally spaced DFE, FF tapped delays are only afraction of one bit time while FB tapped delays are still one bit time.A delay of T/3 for FF tapped delay filters was used for fractionallyspaced DFE. With fractionally spaced DFE, the number of FF tapped delayfilters are increased by three times to include the same number of bitsas in bit synchronous DFE. The performance of 400 km system with thespectral efficiency of 1.6 bit/sec/Hz was compared with 800 km systemwith the spectral efficiency of 1 bit/sec/Hz using bit synchronous andfractionally spaced DFE. The optimum performance of these two systemswas 14.1 and 16 dB of Q at the optimum power levels of −3 and −2dBm/channel, respectively for bit synchronous DFE case (FIG. 6).

These systems were again simulated at these power levels withfractionally spaced DFE (FF tapped delay=T/3). The corresponding resultsare shown in FIG. 7 where the optimal Q values of bit synchronous andfractionally spaced DFE are plotted side by side. The Q improvement is0.6 dB in 400 km system with spectral efficiency of 1.6 bit/sec/Hz,while a Q improvement of only 0.3 dB is obtained in 800 km system withspectral efficiency of 1 bit/sec/Hz. The improvement is slightly betterin the case of spectral efficiency of 1.6 bit/sec/Hz because of more ISIdue to stronger pre-filtering which is better compensated byfractionally spaced DFE.

Various embodiments of the invention have been described for utilizingelectronic signal processing within an optical receiver to compensateISI induced by strong pre-filtering of data at the optical transmitterto enhance the spectral efficiency of an optical communication system,such as a binary NRZ WDM system. In one embodiment, a 10.7 Gb/s WDMsystem employing pre-filtering at the transmitter and electronic signalprocessing at the receiver was analyzed using orthogonal polarizationlaunch for alternate channel wavelengths. A transmission distance of upto 400 km was achievable with this exemplary embodiment with spectralefficiency of up to 1.6 bit/sec/Hz (channel spacing 6.25 GHz) on typicalterrestrial dispersion maps employing standard single mode fiber (SSMF)and erbium doped fiber amplifiers (EDFAs). Channel spacing of 6.25 GHzfor 10.7 Gb/s data rate is otherwise impossible in binary NRZ systemsbecause of severe cross-talk.

The described techniques can be embodied in a variety of opticaltransmitters, receivers, and/or transceivers for optical communicationsystems or networks. The devices may include a general-purposeprocessor, embedded processor, digital signal processor (DSP), fieldprogrammable gate array (FPGA), application specific integrated circuit(ASIC) or similar hardware, firmware and/or software for implementingthe techniques described herein. If implemented in software, acomputer-readable storage medium may store computer readableinstructions, i.e., program code, that can be executed by a processor orDSP to carry out one of more of the techniques described above. Forexample, the computer-readable storage medium may comprise random accessmemory (RAM), read-only memory (ROM), non-volatile random access memory(NVRAM), electrically erasable programmable read-only memory (EEPROM),flash memory, or the like. These and other embodiments are within thescope of the following claims.

1. An optical communication system comprising: a transmitter having a filter that pre-filters each of a plurality of data channels to limit the bandwidth of each of said plurality of data channels and outputs an optical transmission which includes the pre-filtered data channels; and a receiver having an equalizer that applies digital equalization to the optical transmission, said digital equalization configured to compensate for the pre-filtering of the data channels at the transmitter.
 2. The optical communication system of claim 1, wherein said filter cuts off high frequency components associated with said plurality of data channels to generate said pre-filtered data channels having a format that achieves a spectral efficiency that equals or exceeds 1 bit/sec/Hz.
 3. The optical communication system of claim 1, wherein said transmitter further comprises a modulator and wherein the modulator applies a binary modulation format to each of the pre-filtered data channels.
 4. The optical communication system of claim 3, wherein the modulator comprises a non-return to zero (NRZ) intensity modulator.
 5. The optical communication system of claim 1, wherein the filter of the transmitter limits the frequency spreading of each of the data channels in the frequency domain and allows for reduced channel spacing within the optical transmission.
 6. The optical communication system of claim 1, wherein the filter of the transmitter comprises an electrical low pass filter (LPF).
 7. The optical communication system of claim 6, wherein the low pass filter comprises a Bessel shaped LPF of order
 10. 8. The optical communication system of claim 1, wherein the digital equalizer comprises a digital feedback equalizer (DFE).
 9. The optical communication system of claim 8, wherein the DFE electronically compensates for inter-symbol interference (ISI) induced by the pre-filter at the transmitter.
 10. The optical communication system of claim 8, wherein the DFE of the receiver contains n feed forward (FF) and m feedback (FB) tapped delay filters.
 11. The optical communication system of claim 10, wherein n and m are a function of an amount of filtering applied by the filter of the transmitter.
 12. The optical communication system of claim 10, wherein n and m are a function of a channel spacing used by the transmitter for the data channels when outputting the optical transmission.
 13. The optical communication system of claim 10, wherein the DFE of the receiver contains no more than 8 FF and no more than 2 FB tapped delay filters.
 14. The optical communication system of claim 1, wherein the equalizer of the receiver compensates for distortion in the signal that was intentionally introduced at the transmitter.
 15. The optical communication system of claim 1, wherein coefficients of the equalizer are determined as a function of an amount of distortion intentionally introduced within the data channels by the filter of the transmitter.
 16. The optical communication system of claim 1, wherein coefficients of the equalizer are adaptively computed to minimize error within the optical transmission.
 17. The optical communication system of claim 1, wherein the equalizer of the receiver outputs a stream of detected bits from the equalized optical transmission.
 18. The optical communication system of claim 1, wherein the equalizer comprises a Maximum Sequence Likelihood Estimation (MSLE) equalizer or a Viterbi Decoder.
 19. A method comprising: pre-filtering, at an optical transmitter, each of a plurality of data channels to limit a bandwidth for each of the data channels; outputting the pre-filtered data channels from the optical transmitter in the form of an optical transmission; and applying digital equalization to the optical transmission at an optical receiver to compensate for the pre-filtering of the data channels at the transmitter.
 20. The method of claim 19, wherein pre-filtering comprises filtering the plurality of data channels into a format that achieves a spectral efficiency that equals or exceeds 1 bit/sec/Hz.
 21. The method of claim 20, further comprises modulating the pre-filtered data channels by applying a binary modulation format to each of the pre-filtered data channels.
 22. The method of claim 19, wherein pre-filtering comprises applying a low pass filter to limit frequency spreading of each of the data channels so as to allow for reduced channel spacing within the optical transmission.
 23. The method of claim 19, wherein applying digital equalization comprises applying digital feedback equalization (DFE) at the receiver to electronically compensate for inter-symbol interference (ISI) induced by the pre-filtering of the data channels at the transmitter.
 24. The method of claim 23, further comprising selecting a number n of feed forward (FF) and a number m of feedback (FB) tapped delay filters of a digital feedback equalizer of the receiver as a function of an amount of the pre-filtering to the data channels at the transmitter.
 25. The method of claim 23, further comprising selecting a number n of feed forward (FF) and a number m of feedback (FB) tapped delay filters of a digital feedback equalizer of the receiver as a function of a channel spacing used by the transmitter for the data channels when outputting the optical transmission.
 26. The method of claim 23, further comprising selecting coefficients of a digital feedback equalizer of the receiver as a function of an amount of distortion intentionally introduced within the data channels by the filtering of the transmitter.
 27. A computer-readable medium comprising instructions for causing a programmable processor to perform a method of claim
 19. 28. An optical transmitter that pre-filters each of a plurality of data channels prior to modulation of the data channels to limit a bandwidth of each of said plurality of data channels and output of an optical transmission, wherein application of digital feedback equalization to the optical transmission compensates for the pre-filtering of the data channels and allows bit detection.
 29. The method of claim 19, wherein applying digital equalization comprises applying Maximum Sequence Likelihood Estimation (MSLE) or a Viterbi Decoding.
 30. An optical receiver comprising: a photo detector to receive an optical transmission where each of a plurality of data channels prior of the transmission have been pre-filtered to limit a bandwidth of the data channels; and a digital feedback equalizer (DFE) that applies digital feedback equalization to the optical transmission to compensate for the pre-filtering of the data channels at the transmitter. 